Fuzzy logics based on [0,1)-continuous uninorms

TY - JOUR

T1 - Fuzzy logics based on [0,1)-continuous uninorms

AU - Gabbay, D

AU - Metcalfe, G

PY - 2007/7

Y1 - 2007/7

N2 - Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hajek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics

AB - Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hajek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics

U2 - 10.1007/s00153-007-0047-1

DO - 10.1007/s00153-007-0047-1

M3 - Article

SN - 1432-0665

VL - 46

SP - 425

EP - 449

JO - ARCHIVE FOR MATHEMATICAL LOGIC

JF - ARCHIVE FOR MATHEMATICAL LOGIC

IS - 5-6

ER -